Concepts inNonlinear programming on generalized networks
Nonlinear programming
In mathematics, nonlinear programming (NLP) is the process of solving a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are nonlinear.
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Newton's method in optimization
In mathematics, Newton's method is an iterative method for finding roots of equations. More generally, Newton's method is used to find stationary points of differentiable functions, which are the zeros of the derivative function.
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Line search
In optimization, the line search strategy is one of two basic iterative approaches to finding a local minimum of an objective function . The other approach is trust region. The line search approach first finds a descent direction along which the objective function will be reduced and then computes a step size that decides how far should move along that direction. The descent direction can be computed by various methods, such as gradient descent, Newton's method and Quasi-Newton method.
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MINOS (optimization software)
MINOS is a linear and nonlinear mathematical optimization solver that runs with TOMLAB, GAMS, AMPL and AIMMS and a range of other mathematical modelling packages. For linear problems the software employs a simplex method, while for nonlinear problems a reduced-gradient method is used . The software is maintained and was written by Bruce Murtagh, Michael Saunders et al.
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Artificial neural network
An Artificial Neural Network (ANN), usually called neural network (NN), is a mathematical model or computational model that is inspired by the structure and/or functional aspects of biological neural networks. A neural network consists of an interconnected group of artificial neurons, and it processes information using a connectionist approach to computation.
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